Selecting the rank of truncated SVD by Maximum Approximation Capacity

Details Selecting the rank of truncated SVD by Maximum Approximation Capacity Selecting the rank of truncated SVD by Maximum Approximation Capacity

2011-02-15

arxiv.org/abs/1102.3176v3

Computer Science

Information Theory

7 pages, 5 figures; Will be presented at the IEEE International Symposium on Information Theory (ISIT) 2011. The conference ve

Scientific paper

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization problem into a noisy channel coding problem. The optimal approximation capacity of this channel controls the appropriate strength of regularization to suppress noise. In simulation experiments, this information theoretic method to determine the optimal rank competes with state-of-the art model selection techniques.

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